Correlation functions of the XXZ spin-1/2 chain: recent progress
Correlation functions of the XXZ spin-1/2 chain: recent progress
Correlation functions of the XXZ spin-1/2 chain: recent progress
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J. M. Maillet <strong>Correlation</strong> <strong>functions</strong>A very brief history...Three main lines <strong>of</strong> approach have been developped :• Bootstrap methods for <strong>the</strong> form factors + sums over all eigenstates (Karowski, Weisz,Smirnov,....)• Infinite volume + non-abelian quantum symmetries (Jimbo, Miwa,....)• Finite volume + algebraic Be<strong>the</strong> ansatz (Izergin, Korepin,...)−→ More <strong>recent</strong>ly a new approach :Algebraic Be<strong>the</strong> ansatz in finite volume + solution <strong>of</strong> <strong>the</strong> quantum inverse scatteringproblem (Kitanine, Maillet, Terras)−→ At zero temperature, and in <strong>the</strong> <strong>the</strong>rmodynamic limit, it leads to multiple integralrepresentations <strong>of</strong> <strong>the</strong> correlation <strong>functions</strong> for <strong>the</strong> <strong>XXZ</strong> <strong>spin</strong>-1/2 <strong>chain</strong>– Typeset by FoilTEX – Florence 2003 3
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